Differential and Integral Equations

Liouville theorems for integral systems related to fractional Lane-Emden systems in $\mathbb{R}^N_+$

Senping Luo and Wenming Zou

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper, we consider some integral systems in the half space $\mathbb R^N_+$ and obtain Liouville type theorems about the positive solutions. By moving plane method in terms of the integral form, we shall see that the positive solution $(u(x_1,...,x_N), v(x_1,...,x_N))$ of the integral systems must be independent of the first $(N-1)$-variables, i.e., $u=u(x_N),v=v(x_N)$. Then, combine with the order estimates about $x_N$, we reduce the problem to a sequence of algebraic systems. Furthermore, we discuss the relationship between the integral system and the fractional differential system related to the fractional Lane-Emden equations. By this way, we obtain two non-existence theorems for the fractional differential system.

Article information

Differential Integral Equations Volume 29, Number 11/12 (2016), 1107-1138.

First available in Project Euclid: 13 October 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65R20: Integral equations 35B53: Liouville theorems, Phragmén-Lindelöf theorems 35R11: Fractional partial differential equations


Luo, Senping; Zou, Wenming. Liouville theorems for integral systems related to fractional Lane-Emden systems in $\mathbb{R}^N_+$. Differential Integral Equations 29 (2016), no. 11/12, 1107--1138. https://projecteuclid.org/euclid.die/1476369332.

Export citation